#### What are the effects of b on the graph?

**What effect will b have if it is positive?**

As a point of reference, below is the graph
of

b>1

Now let's look at this same equation, but when
b = 2.

The first thing that we notice, is the second
set of petals that are "nested" inside of the 3 petals.
The petals have also been stretched or elongated.

When b=3, will there be 3 sets of petals?

No, there remain only 2 sets of petals. But
the petals are even longer.

So, the value of b greater than 1, creates
a second set of petals, and stretches or elongates the petals.

It is interesting, in this layered graph, there
approaches a point when the tip of the interior petal (from the
graph with a larger value of b) touches the tip of an exterior
petal (from the graph with a smaller value of b).

**What effect will b have if it is a fraction?**

Here is the case where a=1, b=(1/3) and n=3.

Notice, that b affects the graph similar to
the way that a positive value for a might, by moving the graph
farther from the origin.

Notice in this case, where a = 1, n = 3, and
b = (2/3), that the petals have more definition and gets closer
to the origin, than the case where b=1/3.

We can see from this layered graph, that the
closer the value of b gets to 1, the longer the petals are, and
the closer their bases get to the origin.

**What effect will b have if it is negative?**

A negative value for b simply reflects the
graph across the vertical axis.

Click **here**
to return to the Polar Equations main page.

Click **here**
to return to Julie's main page.